| Flow and transportation efficiency of an oscillator chain in Stokes flow |
 粟 偉巍
（指導教員：郡 宏 教授／
数理情報第8研究室）
Most bacteria are driven by the cilia or flagella, consisting of a long filament and a rotary molecular motor through a short flexible hook. The beating pattern of these filaments shows synchronization properties from hydrodynamic interactions especially in low Reynolds number fluids, or the so-called Stokes flow. This thesis introduces a simple spherical rotor, or bead model, which executes oscillatory movement in one dimension by a restoring force, as a simplified imitation of movement by those filaments. It is demonstrated that the flow generated by such model can be enhanced from the hydrodynamic interaction between beads, with supports from both theoretical and numerical results. A reasonable definition efficiency is provided as well, and the efficiency also highly correlates with the hydrodynamic interaction. Increment of the number of beads produces larger hydrodynamic interaction, which contributes to stronger flow and efficiency. In case of the setup with the wall effect involved, the similar laws still hold even more obviously. Finally, the internally driven, or autonomous version of this setup shows interesting phenomena, such as the convergence pattern of phase difference, which even breaks under high coupling strength between beads.
It could be very helpful to derive the theoretical expressions for the displacement and efficiency of the case with Blake's tensor, which could meet more practical usages than the case with Oseen tensor. An autonomous extension is also interesting, especially for phenomena such as the synchronization pattern of multiple bead motors, and to compose a theoretical frame is crucial to deepen the understanding of hydrodynamic effect of interactive objects in low Reynolds number flow.
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